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Find the fifth term of (x^2+y^2)^13.

User Ceelos
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Final answer:

To find the fifth term of (x^2+y^2)^13, we can use the binomial theorem. The fifth term is given by C(13, 4) * x^18 * y^8.

Step-by-step explanation:

To find the fifth term of (x^2+y^2)^13, we can use the binomial theorem. The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n can be found using the formula:

(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n

In this case, a = x^2 and b = y^2, and we want to find the fifth term, so n = 13 and the term number is k = 5.

Plugging in the values, the fifth term is given by:

C(13, 4) * (x^2)^(13-4) * (y^2)^4

Let's simplify this further:

C(13, 4) * x^18 * y^8

User Kenny John Jacob
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